Consider the following initial value problem:

$y^{\text{'}\text{'}}+36y=\{\begin{array}{cc}8,& 0t6\\ 0,& t>6\\ y(0)=7\\ y^{\text{'}}(0)=0\end{array}$

Using $Y$ for the Laplace transform of $y(t),$ i$.$e$.,Y=L\{y(t)\},$ find the equation you get by taking the Laplace transform of the differential equation and solve for

$Y(s)=$